In the situation described, if your husband has done ‘ruju’ (reconciliation) during the ʿiddah (waiting period) after the first two divorces, and then, on the final occasion, he clearly said the words “I divorce you” while fully conscious and in control of his senses, then the third divorce has validly taken place. As a result, ‘ḥurmat-e-mughallaẓah’ (irrevocable prohibition) has been established. After this, neither rujūʿ (reconciliation) nor remarriage between the two of you is permissible.
It should be clearly understood that after three divorces, remarriage is only possible in one specific situation: the woman must complete her ʿiddah, then enter into a nikkah with another man, and sexual intercourse must take place. If that second husband later divorces her of his own choice or passes away, then after completing her ʿiddah, she may choose to remarry her former husband if both agree.
Apart from this situation, remarriage after three divorces is not permitted.
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الدلائل:
القرآن الکریم: (البقرۃ، الآیۃ: 230)
فَاِنۡ طَلَّقَہَا فَلَا تَحِلُّ لَہٗ مِنۡۢ بَعۡدُ حَتّٰی تَنۡکِحَ زَوۡجًا غَیۡرَہٗ ؕ فَاِنۡ طَلَّقَہَا فَلَا جُنَاحَ عَلَیۡہِمَاۤ اَنۡ یَّتَرَاجَعَاۤ اِنۡ ظَنَّاۤ اَنۡ یُّقِیۡمَا حُدُوۡدَ اللّٰہِ ؕ وَ تِلۡکَ حُدُوۡدُ اللّٰہِ یُبَیِّنُہَا لِقَوۡمٍ یَّعۡلَمُوۡنَ.
صحیح البخاری: (2014/5، ط: دار ابن کثیر )
عن عائشة: أن رجلا طلق امرأته ثلاثا، فتزوجت فطلق، فسئل النبي صلى الله عليه وسلم: أتحل للأول؟ قال: (لا، حتى يذوق عسيلتها كما ذاق الأول).
Allah the Almighty knows best.
Darul ifta Al-Ikhlas, Karachi.